Hi,
sorry, we didn't think it necessary to add more details since it seems fairly easy to reproduce and happens in all the tests we did so far.
As in our last message, to see the issue all you have to do is: fresh Joomla, install HS3, add a product, add two shipping methods and go to checkout - nothing more. It is then impossible to select the second shipping method, that is, we can click the second method but it automatically keeps switching back to the first method.
In the database it also does not change to the second shipping method. Even if we manually change the cart_shipping_ids to the second shipping method, it still shows the first one as selected in the checkout.
We also tried re-ordering the shipping methods so the second method will then appear at the top in the checkout, then it keeps stuck at this one, so doesn't make any difference.
And as we wrote regarding the Legacy mode: you can try turning the legacy modes off, and then turn them back on again, in our case it completely "breaks" the checkout in that we can no longer select any shipping or payment methods. And we haven't figured out any way to fix it yet, except starting all over with a new install of Hikashop.
Hope it's a bit clearer.
Kind regards,